Question

gh || ef. complete the proof that △egh ≅ △gef.
1 gh || ef given
2 gh ≅ ef given
3 ∠egh ≅ ∠feg
4 eg ≅ eg
5 △egh ≅ △gef sas

Explanation:

Step1: Alternate interior angles

Since \( \overline{GH}\parallel\overline{EF}\), by the alternate - interior angles theorem, when a transversal \(EG\) intersects two parallel lines \(GH\) and \(EF\), \( \angle EGH\cong\angle FEG\).

Step2: Reflexive property

For any segment \(EG\), by the reflexive property of congruence, \( \overline{EG}\cong\overline{EG}\) (a segment is congruent to itself).

Answer:

1. Alternate - interior angles theorem; 4. Reflexive property of congruence.